Chapter 5.2, Problem 91E

College enrollment. The projected rate of increase in enrollment at a new college is estimated by

     $\begin{array}{cc}\frac{dE}{dt}=5,000{\left(t+1\right)}^{-3/2}& t\ge 0\end{array}$

where E(t) is the projected enrollment in t years. If enrollment is 2,000 now (t = 0), find the projected enrollment 15 years from now.